Liquid-infused surfaces (LISs) offer an alternative to SHSs where the SHS pockets are filled with a lubricating immiscible fluid instead of gas [1]}, [2]}.
They can self-repair and are most robust than SHSs if properly designed. However, the drag reduction of LISs decreases as the viscosity ratio between internal and external fluids increases [3]}.
Furthermore, recent numerical simulations by [4]} have indicated that LISs may be more susceptible to surfactant effects than SHSs.
[4]} extended the theory introduced in [6]} to account for surfactants in a 2D shear flow, predicting the critical surfactant concentration for the slip to be reduced appreciably: \(\hat{C}_c =4\times 10^{-4}\,\) mol/m\(^3\)  for water–air SHSs and \(\hat{C}_c = 5\times 10^{-5}\,\) mol/m\(^3\)  for water–dodecane LISs.
For low applied shear stresses, [4]} found that the distribution of surfactant at the interface is approximately linear and a scaling theory was used to derive an expression for the slip length.
For high applied shear stresses, surfactant accumulates at the downstream stagnation point and forms a stagnant cap.
[4]} employed numerical simulations to find that the stagnant cap regime only exists below a particular bulk concentration (and above which the scaling theory once again becomes valid).
Considering a typical surfactant, e.g., sodium dodecyl sulfate (SDS), the critical bulk concentration is shown to be proportional to the inverse Marangoni number.
No theory was proposed by [4]} to model and explain the stagnant cap regime where advection dominates.
